a theoretical introduction to numerical analysis

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A Theoretical Introduction To Numerical Analysis

Author : Victor S. Ryaben'kii
ISBN : 1584886072
Genre : Mathematics
File Size : 90. 45 MB
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A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

An Introduction To Numerical Analysis

Author : Endre Süli
ISBN : 0521007941
Genre : Mathematics
File Size : 62. 34 MB
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Introduction to numerical analysis combining rigour with practical applications. Numerous exercises plus solutions.

Introduction To Numerical Analysis

Author : Arnold Neumaier
ISBN : 0521336104
Genre : Mathematics
File Size : 29. 30 MB
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This 2001 textbook provides an introduction to constructive methods that provide accurate approximations to the solution of numerical problems using MATLAB.

Introduction To Numerical Analysis Using Matlab

Author : Rizwan Butt
ISBN : 076377376X
Genre : Mathematics
File Size : 56. 42 MB
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Part of the new Digital Filmmaker Series! Digital Filmmaking: An Introductionis the first book in the newDigital Filmmaker Series. Designed for an introductory level course in digital filmmaking, it is intended for anyone who has an interest in telling stories with pictures and sound and won't assume any familiarity with equipment or concepts on the part of the student. In addition to the basics of shooting and editing, different story forms are introduced from documentary and live events through fictional narratives. Each of the topics is covered in enough depth to allow anyone with a camera and a computer to begin creating visual projects of quality.

Introduction To Numerical Analysis

Author : F. B. Hildebrand
ISBN : 9780486318554
Genre : Mathematics
File Size : 50. 43 MB
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Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.

Introduction To Numerical Analysis

Author : Josef Stoer
ISBN : 9781475755923
Genre : Mathematics
File Size : 35. 93 MB
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This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Theoretical Numerical Analysis

Author : Peter Linz
ISBN : 0486417085
Genre : Mathematics
File Size : 73. 68 MB
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Concise text introduces numerical analysis as a practical, problem-solving discipline, focusing on fundamentals of functional analysis and approximation theory, the major results of theoretical numerical analysis; and specific topics that illustrate the power and usefulness of theoretical analysis. Ideal for use in a one-year graduate course, the text also offers engineers and scientists a simple introduction to major ideas of modern numerical analysis. A knowledge of advanced calculus is assumed.

Introduction To Numerical Methods In Differential Equations

Author : Mark H. Holmes
ISBN : 9780387681214
Genre : Mathematics
File Size : 62. 33 MB
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This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

Numerical Analysis

Author : H. R. Schwarz
ISBN : UCSD:31822003700358
Genre : Mathematics
File Size : 51. 64 MB
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An introduction to numerical analysis, featuring an algorithmic approach. Provides the theoretical basis of each technique, then develops algorithms that are easily implemented on any personal computer. Methods of numerical analysis covered include systems of linear equations, linear programming, interpolation, approximation, and the finite element method. Contains many exercises and worked examples.

A Brief Introduction To Numerical Analysis

Author : Eugene E. Tyrtyshnikov
ISBN : 0817639160
Genre : Education
File Size : 34. 84 MB
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This is an advanced textbook based on lectures delivered at the Moscow Physico-Technical Institute. Brevity, logical organization of the material, and a sometimes lighthearted approach are distinctive features of this modest book. The author makes the reader an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis in a short time. Since matrix analysis underlies numerical methods and the author is an expert in this field, emphasis in the book is on methods and algorithms of matrix analysis. Also considered are function approximations, methods of solving nonlinear equations and minimization methods. Alongside classical methods, new results and approaches developed over the last few years are discussed - namely those on spectral distribution theory and what it gives for design and proof of modern preconditioning strategies for large-scale linear algebra problems. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful. It can be equally useful for advanced readers and researchers in providing them with new findings and new accessible views of the basic mathematical framework.

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